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# Support vector machines

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Support vector machines (SVMs) are a family of machine learning methods, originally introduced for the problem of classification and later generalized to various other situations. They are based on principles of statistical learning theory and convex optimization, and are currently used in various domains of application, including bioinformatics, text categorization, and computer vision. Copyright © 2009 John Wiley & Sons, Inc.

Figure 1.

A separating hyperplane for two‐dimensional data points; the circles and the squares represent, respectively, data points in classes − 1 and + 1. On the dotted lines, in black, lie the support vectors. The margin γ, b, and \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\mathbf{w}$\end{document} are also reported.

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Figure 2.

Two‐dimensional data points that cannot be linearly separated; the circles and the squares, respectively, represent data points in classes − 1 and + 1.

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Figure 3.

These learning curves have been obtained using SVMs with a linear kernel and two polynomial kernels, respectively, with degrees 2 and 3. Among all experiments, the results relative to digit 8 is reported. This is because it better highlights how different kernel functions can produce different performance.

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